A coupled compressible two-phase flow with the biological dynamics modeling the anaerobic biodegradation process of waste in a landfill

: pp. 483–500
Received: November 03, 2021
Accepted: March 23, 2022
University of Haute-Alsace, University of Strasbourg, France
Ibn Tofail University, Equipe d’Ingénierie Mathématique (EIMA), Laboratory: EDP, Algèbre et Géométrie Spectrale, Kénitra, Morocco
University of Haute-Alsace, France; Ibn Tofail University, Equipe d’Ingénierie Mathématique (EIMA), Laboratory: EDP, Algèbre et Géométrie Spectrale, Kénitra, Morocco

In this article, we present and study a new coupled model combining the biological and the mechanical aspects describing respectively the process of the biogas production and the compressible two-phase leachate-biogas flow during the anaerobic biodegradation of organic matters in a landfill, which is considered a reactive porous medium.  The model obtained is governed by a reaction-diffusion system for the bacterial activity coupled with a compressible two-phase flow system of a non-homogeneous porous medium.  We carry out the analysis and the numerical approximation of the model within a variational framework.  We propose a full discrete system based on a second-order BDF-time scheme and P1-conforming finite element and we derive an efficient algorithm for the coupled system.  We perform some numerical simulations in 2D and 3D examples in agreement with the theoretical analysis.

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Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 483–500 (2022)